Inaugurations of American presidents are optimistic occasions, and for good reason. We often forget that peaceful transitions of power in history have been relatively rare, and still are, even in an age of republics. Most people living today won't see an orderly, lawful transition — or continuation — of a representative government under the rule of law. Regardless of your political persuasion, the quadrennial American tradition dating back to 1792 should fill all of us with optimism and appreciation for the blessings of a functional and stable representative republic.

Still, it's possible to overshoot the mark at such events. CBS interviewed House Majority Leader Eric Cantor (R-Va.) during the inauguration's preliminary festivities, and asked him about the prospects for the next two years. Norah O'Donnell noted that House Republicans seemed to have taken a more conciliatory attitude after their caucus retreat last week, with a promise to raise the debt ceiling for a short period of time, and asked Cantor whether that indicated that the GOP would cooperate with President Obama on his second-term agenda.

Cantor told O'Donnell that the election sent a message to both ends of Pennsylvania Avenue that they wanted a change to a functional government that gets things done. "I think that there's an expectation coming out of the election," Cantor replied, "that the American people are going to see a federal government that works." If that was the expectation, then the American people have a funny way of expressing it. The last two years were notable for the gridlock that repeatedly resulted in kicking cans down the road, and yet the American people returned the exact same leadership to Washington in the election two months ago.

The message from November seemed to be exactly the opposite of what Cantor suggested. Remember: Republicans won the House in 2010 in large measure as a reaction to Obama's agenda in the first two years. The grassroots movement that pushed the GOP to its best midterm showing in 72 years didn't come with a mandate to cooperate with Obama and find a middle ground. The Tea Party-driven electorate wanted the Republican Party to stop the Obama agenda, which they succeeded in doing, and to force Obama to accept spending cuts and reductions in federal reach, which they mostly failed to achieve. Instead, the Senate refused to pass budgets, and the result was the continuation of self-inflicted crises of "cliffs" for the past two years.

It's true that the most contentious of these issues, the Bush-era tax rates, got resolved earlier this month by the previous session of Congress before it adjourned. However, that crisis had a definitive time bomb built into it — the expiration of all rate rollbacks and the AMT patch. The latter would have created a massive tax increase on as many as 30 million households. The economic and political damage from that would have impacted both political parties, which pushed them into a last-minute deal that could easily have been concluded two years ago, when the rates first expired.

On the other hand, there have been some recent signs that both sides want to get some of these long-running debates off the table.  Republicans want a normal-order budget with real spending cuts, and preferably some significant start to entitlement reform. Democrats want more revenue, despite winning the fight on the high-earner tax rates, to cushion the blow on entitlement reform.  There is room to have both parties succeed in their goals and still make progress on greatly reducing deficit spending and unfunded liabilities for entitlement programs, two of the greatest long-term threats to American prosperity.

Republicans moved first to supply an opening. The Hill reported in the midst of the inaugural celebration that the House would propose suspending the debt ceiling until mid-May rather than increasing it. This would allow the Treasury to borrow for a short window without having a cap on debt it can issue. In the meantime, that gives Congress time to finish the FY2013 budget, which currently is running on a continuing resolution that expires on March 27, and produce a full budget for FY2014. The House would commit to approving the borrowing done in the meantime along with raising the debt ceiling to accommodate the borrowing needed for the FY2014 budget to move from crisis management back to normal order. In exchange, they want real cuts beyond the sequester from the 2011 agreement, including entitlement reforms.

Democrats want to pass comprehensive tax reform to increase revenues, for which they need normal-order budgeting, for political if not parliamentary reasons. Republicans have an interest in reforming the tax code as well: Broadening the tax base and removing the distortions that come from social engineering in the tax code. With revenue increases from a broadened tax base that will result from real tax-code reform, Democrats should be able to marry that to entitlement reforms that at least begin to reduce the juggernaut of future unfunded liabilities for the federal government. That would produce enough mutual benefit to find a middle ground for both parties that can easily be projected in principle from almost any vantage point on the political spectrum.

This will only happen when both sides see short-term political advantage in consolidating some gains and backing off of all-or-nothing demands, through cooperation and normal order, over obstructionism and brinksmanship. Republicans, who had hoped to have increased leverage after the November elections, appear to have seen the reality of having control of only one lever of power in Washington (the House) while Democrats have the other two (the Senate and White House), and have accordingly adjusted their approach. Will Democrats adjust theirs now that they realize they can't dictate outcomes either, and return to the normal-order budgeting needed to end the Age of Cliffs? That is the question, and it remains to be seen whether Cantor's optimism is an artifact of a sunny day or the acknowledgment of a changed Washington.